Question

A ladder is placed against a wall such that its foot is at distance of 5 m from the wall

and its top reaches a window 5/3 m above the ground. Find the length of the ladder​

Answer 1

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Answer 2

Correct Question :

A ladder is placed against a wall such that its foot is at distance of 5 m from the wall and its top reaches a window 5√3 m above the ground. Find the length of the ladder.

Solution :

Distance of foot from the ladder : 5 m

Height = 5√3 m

The placed ladder,the ground and the wall forms a right angled triangle.

We will solve further using Pythagoras Theorem

$\star \rm \: ( Hypotenuse)^{2} = ( {Perpendicular})^{2} + ({Base})^{2}$

Here,

Hypotenuse is the length of the ladder.

Therefore,

$\sf \hookrightarrow \: (Length \: of \:ladder) ^{2} = \\ \sf({Height})^{2} + (Distance) ^{2}$

$\sf \hookrightarrow \: (Length \: of \:ladder) ^{2} = ( 5\sqrt{3} ) ^{2} + {5}^{2}$

$\sf \hookrightarrow \: (Length \: of \:ladder) ^{2} =( 25 \times 3) + 25$

$\sf \hookrightarrow \: (Length \: of \:ladder) ^{2} = 75 + 25$

$\sf \hookrightarrow \: (Length \: of \:ladder) ^{2} =100 \: m$

$\sf \hookrightarrow \: Length \: of \:ladder = \sqrt{100 \: m}$

$\sf \hookrightarrow \: Length \: of \:ladder = \sqrt{10 \times 10\: m}$

$\sf \hookrightarrow \: Length \: of \:ladder = \large \boxed{ \sf \: 10 \: m}$